My neighbour has planted some laurel hedging up against the wall of my 1750s listed cottage (my wall goes into their garden). I am on clay soil . Should I be worried since there are very shallow foundations
The East of England
We had a laurel hedge. Was at the front of the garden, so quite some distance from the property. We cut off all of the foliage, leaving maybe 2 ft tall trunks only. It all grew back. Eventually we took them out, roots had gone a good 12 ft up the garden!
I don't think this was a particularly sensible decision by your neighbour, to be honest.
However, portugese laurel, prunus lusitanica seems to be much less of a problem. Keep the foliage tightly clipped and the roots won't get that big.